Theory of Projections
Projection theory
In engineering, 3-dimensonal objects
and structures are represented graphically on a 2-dimensional media. The act of
obtaining the image of an object is termed “projection”. The image
obtained by projection is known as a “view”. A simple projection system
is shown in figure 1.
All projection theory are based on
two variables:
·
Line of sight
·
Plane of
projection.
Plane of Projection
A plane of projection (i.e, an image
or picture plane) is an imaginary flat plane upon which the image created by
the line of sight is projected. The image is produced by connecting the
points where the lines of sight pierce the projection plane. In effect, 3-D
object is transformed into a 2-D representation, also called projections. The
paper or computer screen on which a drawing is created is a plane of
projection.
Projection Methods
Projection methods are very important
techniques in engineering drawing.
Two projection methods used are:
·
Perspective and
·
Parallel
the observer is assumed to be
stationed at finite distance from the object. The height of the buildings
appears to be reducing as we move away from the observer. In perspective
projection, all lines of sight start at a single point and is schematically
shown in figure.
In parallel projection, all lines of sight are parallel and is
schematically represented in figure. 4. The observer is assumed to be stationed
at infinite distance from the object.
Parallel projection
√ Distance from the observer to the
object is infinite projection lines are parallel – object is positioned at
infinity.
√ Less realistic but easier to draw.
Perspective projection
·
Distance from the observer to the object is finite and the object is
viewed from a single point – projectors are not parallel.
·
Perspective projections mimic what the human eyes see, however, they are
difficult to draw.
Orthographic Projection
Orthographic projection is
a parallel projection technique in which the plane of projection is
perpendicular to the parallel line of sight. Orthographic projection technique
can produce either pictorial drawings that show all three dimensions of an
object in one view or multi-views that show only two dimensions of an object in
a single view. These views are shown in figure
Transparent viewing box
Assume that the object is placed in a
transparent box, the faces of which are orthogonal to each other, as shown in
figure . Here we view the object faces normal to the three planes of the
transparent box.
When the viewing planes are
parallel to these principal planes, we obtain the Orthographic views
The picture we obtain when the line of sight is projected on to each plane is
called as the respective view of the object. The image obtained on the
projection planes , i.e., on the top face, Front Face, and Right side
face are respectively the Top View, Front view and Right side view
of the object and is shown in figure
Multi-view Projection
In an orthographic projection, the
object is oriented in such a way that only two of its dimensions are shown. The
dimensions obtained are the true dimensions of the object .
Frontal plane of projection
Frontal plane of projection is the
plane onto which the Front View (FV) of the multi-view drawing is
projected.
Figure illustrates the method of obtaining the Front view of an object. Front view of an object shows the width and height dimensions.
Figure illustrates the method of obtaining the Front view of an object. Front view of an object shows the width and height dimensions.
Horizontal plane of projection
Horizontal plane of projection is the
plane onto which the Top View of the multi-view drawing is projected and is
shown in Figure . The Top view of an object shows the width and depth
dimensions of the object.
Profile plane of projection
In multi-view drawings, the right
side view is the standard side view used and is illustrated in figure.
The right side view of an object shows the depth and the height
dimensions. The right side view is projected onto the profile plane of
projection, which is a plane that is parallel to the right side of the object.
Orientation of views from projection
planes
Multi-view drawings gives the
complete description of an object. For conveying the complete information, all
the three views, i.e., the Front view, Top view and side view of the object is
required. To obtain all the technical information, at least two out of the
three views are required. It is also necessary to position the three
views in a particular order. Top view is always positioned and aligned with the
front view, and side view is always positioned to the side of the Front view
and aligned with the front view. The positions of each view is shown in figure
11. Depending on whether 1st angle or 3rd angle
projection techniques are used, the top view and Front view will be interchanged.
Also the position of the side view will be either towards the Right or left of
the Front view.
Six Principal views
The plane of projection can be
oriented to produce an infinite number of views of an object. However,
some views are more important than others. These principal views are the
six mutually perpendicular views that are produced by six mutually
perpendicular planes of projection and is shown in figure Imagine
suspending an object in a glass box with major surfaces of the object
positioned so that they are parallel to the sides of the box, six sides of the
box become projection planes, showing the six views – front, top, left, right,
bottom and rear.
Object is suspended in a glass box
producing six principal views: each view is perpendicular to and aligned with
the adjacent views.
The glass box is now slowly unfolded
as shown in figure. After complete unfolding of the box on to a single
plane, we get the six views of the object in a single plane as shown in figure. The top, front and bottom views are all aligned vertically and share the
same width dimension where as the rear, left side, front and right side views
are all aligned horizontally and share the same height dimension.
Conventional view placement
The three-view multi-view drawing is the standard used in engineering and technology, because many times the other three principal views are mirror images and do not add to the knowledge about the object. Figure shows the standard views used in a three-view drawing i.e., the top, front and the right side views
The three-view multi-view drawing is the standard used in engineering and technology, because many times the other three principal views are mirror images and do not add to the knowledge about the object. Figure shows the standard views used in a three-view drawing i.e., the top, front and the right side views
The width dimensions are aligned
between the front and top views, using vertical projection lines. The height
dimensions are aligned between the front and the profile views, using
horizontal projection lines. Because of the relative positioning of the
three views, the depth dimension cannot be aligned using projection lines.
Instead, the depth dimension is measured in either the top or right side view.
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